arXiv subjects

J. A. Sheikh

Publications and source records attributed to J. A. Sheikh.

At least 19 recordsLinked to original sources

arXiv2026

Low lying excitations in $^{150}$Pm

The low lying excitations in odd-odd $^{150}$Pm have been studied through proton induced reaction with an array of five Compton suppressed Clover HPGe and one segmented planar Ge detectors. The relative excitation functions for the observed $\gamma$ rays have been studied using singles data at two beam energies of 8~MeV and 9~MeV. 16 new $\gamma$ rays and 15 new levels have been placed in the level scheme of $^{150}$Pm based on $\gamma-\gamma$ coincidence data. The relative intensities for the observed $\gamma$ rays have been determined using total and gated projections. Tentative spin-parity assignments were made to few low lying excitations of $^{150}$Pm, using limited angular distribution data and other information. Lifetimes were estimated for two excited levels in this nucleus using using generalized centroid difference analysis, applied in the nanosecond range, with Ge detectors. Large basis shell model and projected shell model calculation were performed to interpret the experimentally observed levels. The present work indicates 1$^-$ ground state, a 2$^-$ state close to the ground state ($\sim$50~keV) and a low lying 6$^-$ isomeric state in this odd-odd nucleus along with emerging band structures developed with two quasiparticle configurations.

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arXiv2026

Microscopic investigation of $E2$ matrix elements in atomic nuclei -- II

The present work is a continuation of our earlier investigation with the primary objective to systematically calculate the $E2$ matrix elements using the microscopic approach of the triaxial projected shell model (TPSM). In the earlier work, we studied nine nuclides of $^{72}$Ge, $^{76}$Ge, $^{104}$Ru, $^{168}$Er, $^{186}$Os, $^{188}$Os, $^{190}$Os, $^{192}$Os, and $^{194}$Pt. In the present work six more nuclides of $^{70}$Ge, $^{76,78,80,82}$Se, and $^{100}$Mo have been investigated. The Coulomb excitation data has recently become available for $^{70}$Ge and other nuclides were inadvertently omitted in our earlier investigation. It is demonstrated that TPSM approach provides a good description of the available experimental data and most of the nuclides, except for $^{76}$Se and $^{100}$Mo, are shown to have $\gamma$ soft behaviour. Further, it is demonstrated that in contrast to the predictions of the phenomenological collective model, TPSM calculations depict no clear correlation between the energy staggering pattern of the $\gamma$ band and the deduced shape invariant quantities using the Kumar-Cline sum rules.

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arXiv2026

Microscopic investigation of $\gamma~$ vibrational band structures in odd-mass nuclei

A systematic investigation of the high-spin band structures observed in $^{103,105,107,109}$Nb and $^{103,105,107,109}$Tc nuclides is performed using the triaxial projected shell model (TPSM) approach. For $^{103,105}$Nb isotopes, four bands have been populated with the lowest three bands corresponding to yrast, $\gamma$ and 2$\gamma$ bands. The nature of the fourth observed band has remained unresolved as it has been shown from the transition intensity ratios that this band cannot correspond to the expected 3$\gamma$ band. It is demonstrated in the present work that this fourth band is the second $\gamma$ band, resulting from the combination, $K=K_0-2$ with $K_0$ being the "$K$" value of the parent configuration. The excitation energy and other properties of this band structure are predicted for all the studied nuclides.

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arXiv2026

First observation of multi-phonon $\gamma$-vibrations in an odd-odd nuclear system

The identification of the first multi-phonon $\gamma$-vibrational bands in an odd-odd neutron-rich nucleus of the nuclear chart is presented. These high spin structures of hard to access $^{104}_{41}$Nb$_{63}$, produced in fission, were studied by combining a spectrometer with isotopic resolution coupled to a $\gamma$-ray tracking array and independently high-fold $\gamma$ coincidence measurements. Triaxial Projected Shell Model calculations for the high-spin states are in good agreement with the measured observables for the yrast, one-phonon and two-phonon $\gamma$ bands. The possibility of an oblate shape of an isomeric state and coexistence of triaxial and oblate configurations are investigated from the decay of the 141 keV isomer. The present work illustrates the robustness of vibration excitations in the presence of odd valence proton and neutron as well as the possibly coexisting shapes beyond the $N=60$ transitional region.

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arXiv2026

Microscopic investigation of magnetic and antimagnetic rotational motion in atomic nuclei

In the present work, we have generalized the projected shell model (PSM) approach to include the quasiparticle excitations from two major oscillator shells, and have also extended the basis space to five-quasiparticle configurations for odd-mass nuclei. The magnetic and antimagnetic rotational structures observed in odd-neutron Pd- and Cd-isotopes have been investigated as a first major application of the new development. It is shown that PSM approach provides a reasonable description of the observed properties of magnetic and antimagnetic rotational bands.

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arXiv2025

Microscopic investigation of wobbling motion in even-even nuclei

The possibility of observing wobbling mode in the even-even systems of 76Ge, 112Ru, 188,192Os, 192Pt and 232Th is explored using the triaxial projected shell model approach. These nuclei are known to have {\gamma}-bands whose odd-spin members are lower than the average of the neighbouring even-spin states. It is shown through a detailed analysis of the excitation energies and the electromagnetic transition probabilities that the observed band structures in these nuclei except for 232Th can be characterised as originating from the wobbling motion. It is further demonstrated that quasiparticle alignment is responsible for driving the systems to the wobbling mode.

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arXiv2025

Microscopic investigation of $E2$ matrix elements in atomic nuclei

A systematic analysis of $E2$ matrix elements of $^{72}$Ge, $^{76}$Ge, $^{168}$Er, $^{186}$Os, $^{188}$Os, $^{190}$Os, $^{192}$Os and $^{194}$Pt nuclides is performed using the beyond mean-field approach of triaxial projected shell model (TPSM). For these nuclei, large sets of $E2$ matrix elements have been deduced from the multi-step Coulomb excitation experiments, and it is shown that TPSM approach provides a reasonable description of the measured transitions. We have evaluated 1496 $E2$ matrix elements up to spin, $I=10$ for the eight nuclei studied, and tabulate them for future experimental and theoretical comparisons. Further, shape invariant analysis has been performed with the calculated $E2$ transitions using the Kumar-Cline sum rules. It is inferred from the analysis that the resulting shape, after configuration mixing of the quasiparticle states, transforms from $\gamma$-rigid to that of $\gamma$-soft for some nuclei, in conformity with the experimental data.

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arXiv2024

Measurement of enhanced electric dipole transition strengths at high spin in $^{100}$Ru: Possible observation of octupole deformation

The majority of atomic nuclei have deformed shapes and nearly all these shapes are symmetric with respect to reflection. There are only a few reflection asymmetric pear-shaped nuclei that have been found in actinide and lanthanide regions, which have static octupole deformation. These nuclei possess an intrinsic electric dipole moment due to the shift between the center of charge and the center of mass. This manifests in the enhancement of the electric dipole transition rates. In this article, we report on the measurement of the lifetimes of the high spin levels of the two alternate parity bands in $^{100}$Ru through the Doppler Shift Attenuation Method. The estimated electric dipole transition rates have been compared with the calculated transition rates using the triaxial projected shell model without octupole deformation, and are found to be an order of magnitude enhanced. Thus, the observation of seven inter-leaved electric dipole transitions with enhanced rates establish $^{100}$Ru as possibly the first octupole deformed nucleus reported in the A $\approx$ 100 mass region.

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arXiv2024

Microscopic investigation of wobbling motion in atomic nuclei using the triaxial projected shell model approach

A systematic investigation of the wobbling band structures observed in odd-mass nuclei of $^{161,163,165,167}$Lu, $^{167}$Ta $^{131}$Cs, $^{135}$Pr, $^{151}$Eu, $^{183}$Au, $^{133}$Ba, $^{105}$Pd, $^{133}$La, $^{187}$Au and $^{127}$Xe is performed using the triaxial projected shell model (TPSM) approach. It is demonstrated that all the studied band structures have transverse wobbling mode, except for $^{133}$La, $^{187}$Au (negative parity), $^{183}$Au (positive parity) and $^{127}$Xe nuclei where the wobbling frequency increases with spin, indicating that the collective motion has a longitudinal character. To elucidate further the wobbling nature of the band structures, electromagnetic transition probabilities have been evaluated and it is observed that inter-band transitions are dominated by $E2$ rather than $M1$ as expected for a typical signature partner band. It is shown that TPSM approach provides a reasonable description of all the measured properties of the studied nuclei.

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arXiv2024

Isospin symmetry breaking in atomic nuclei

The importance of the isospin symmetry and its breaking in elucidating the properties of atomic nuclei is reviewed. The quark mass splitting and the electromagnetic origin of the isospin symmetry breaking (ISB) for nuclear many-body problem is discussed. The experimental data on isobaric analogue states cannot be described only with the Coulomb interaction, and ISB terms in the nucleon-nucleon interaction are needed to discern the observed properties. In the present work, the ISB terms are explicitly considered in nuclear energy density functional and spherical shell model approaches, and a detailed investigation of the analogue states and other properties of nuclei is performed. It is observed that isospin mixing is largest for the $N=Z$ system in the density functional approach.

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arXiv2024

First identification of a doublet wobbling excitation mode in $^{105}$Pd

An experimental investigation of $^{105}$Pd has revealed, for the first time, the existence of two wobbling bands, both having one phonon configuration and originating from excitation which is the wobbling from the yrast band with the $h_{11/2}$ quasineutron fully aligned with the short axis, and from an excited band with the same quasineutron but with less alignment along the short axis. These observations have been drawn from the measured ratios of the inter-band and intra-band gamma transition rates. Model calculations based on the triaxial projected shell model (TPSM) approach have been performed and are found to be in good agreement with the experimental energies and relative transition probabilities. The analysis of the TPSM results provides an insight into the nature of the observed structures at a microscopic level.

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arXiv2024

Fingerprints of the triaxial deformation from energies and $B(E2)$ transition probabilities of $γ$-bands in transitional and deformed nuclei

The energies and $B(E2)$ transitions involving the states of the ground- and $γ$-bands in thirty transitional and deformed nuclei are calculated using the triaxial projected shell model (TPSM) approach. Systematic good agreement with the existing data substantiates the reliability of the model predictions. The Gamma-rotor version of the collective Bohr Hamiltonian is discussed in order to quantify the classification with respect to the triaxial shape degree of freedom. The pertaining criteria are applied to the TPSM results and the staggering of the energies of the $γ$-bands is analyzed in detail. An analog staggering of the intra-$γ$ $B(E2,I\rightarrow I-2)$ is introduced for the first time. The emergence of the staggering phenomena in the transitions is explained in the terms of interactions between the bands.

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arXiv2023

Triaxial projected shell model approach for negative parity states in even-even nuclei

The triaxial projected shell model (TPSM) approach is generalized to investigate the negative parity band structures in even-even systems. In the earlier version of the TPSM approach, the quasiparticle excitations were restricted to one major oscillator shell and it was possible to study only positive parity states in even-even systems. In the present extension, the excited quasiparticles are allowed to occupy two major oscillator shells, which makes it possible to generate the negative parity states. As a major application of this development, the extended approach is applied to elucidate the negative parity high-spin band structures in $^{102-112}$Ru and it is shown that energies obtained with neutron excitation are slightly lower than the energies calculated with proton excitation. However, the calculated aligned angular momentum ($i_x$) clearly separates the two spectra with neutron $i_x$ in reasonable agreement with the empirically evaluated $i_x$ from the experimental data, whereas proton $i_x$ shows large deviations. Furthermore, we have also deduced the transition quadrupole moments from the TPSM wavefunctions along the negative-parity yrast- and yrare- bands and it is shown that these quantities exhibit rapid changes in the bandcrossing region.

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arXiv2022

Microscopic aspects of $γ$-softness in atomic nuclei

The microscopic origin of the $γ$-softness (fluctuations in the triaxiality parameter $γ$ of the nuclear shape) observed in atomic nuclei is studied in the framework of the triaxial projected shell model approach, which is based on the deformed mean-field picture with multi-quasiparticle configuration space. It is demonstrated that the coupling to quasiparticle excitations drives the system from a $γ$-rigid to a $γ$-soft pattern. As an illustrative example for a $γ$-soft nucleus, a detailed study has been performed for the $^{104}$Ru nucleus. The experimental energies and a large sample of measured $E2$ matrix elements available for this nucleus are reproduced quite accurately. The shape invariant analysis of the calculated $E2$ matrix elements elucidates the $γ$-soft nature of $^{104}$Ru.

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arXiv2022

Extended triaxial projected shell model approach for odd-neutron nuclei

In an effort to elucidate the rich band structures observed in odd-neutron systems, triaxial projected shell model approach is extended to include three-quasineutron and five-quasiparticle configurations. This extension makes it possible to investigate the high-spin states up to and including the second band crossing. Detailed investigation has been performed for odd-mass Xe isotopes with the extended basis, and it is shown that character of the band crossing along the yrast line changes with shell filling of the 1h11/2 orbital. Further, it is observed that the three-quasiparticle state that crosses the ground-state configuration, leading to the normal band crossing phenomenon along the yrast line, first crosses the γ band based on the ground-state configuration at an earlier spin value. This crossing feature explains the occurrence of the signature inversion observed in the γ bands for some of the studied isotopes.

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arXiv2021

Symmetry restoration in mean-field approaches

The mean-field approximation based on effective interactions or density functionals plays a pivotal role in the description of finite quantum many-body systems that are too large to be treated by ab initio methods. Some examples are strongly interacting medium and heavy mass atomic nuclei and mesoscopic condensed matter systems. In this approach, the linear Schrodinger equation for the exact many-body wave function is mapped onto a non-linear density-dependent one-body potential problem. This approximation, not only provides computationally very simple solutions even for systems with many particles, but due to the non-linearity, it also allows for obtaining solutions that break essential symmetries of the system, often connected with phase transitions. In this way, additional correlations are subsumed in the system. However, the mean-field approach suffers from the drawback that the corresponding wave functions do not have sharp quantum numbers and, therefore, many results cannot be compared directly with experimental data. In this article, we discuss general group-theory techniques to restore the broken symmetries, and provide detailed expressions on the restoration of translational, rotational, spin, isospin, parity and gauge symmetries, where the latter corresponds to the restoration of the particle number. In order to avoid the numerical complexity of exact projection techniques, various approximation methods available in the literature are examined. Applications of the projection methods are presented for simple nuclear models, realistic calculations in relatively small configuration spaces, nuclear energy density functional theory, as well as in other mesoscopic systems. Further, unresolved problems in the application of the symmetry restoration methods to the energy density functional theories are highlighted in the present work.

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arXiv2021

Systematic study of near yrast band structures in odd-mass $^{125-137}$Pr and $^{127-139}$Pm isotopes

In the present work, the basis space in the triaxial projected shell model approach is expanded to include three and five quasiparticle configurations for odd-proton systems. This extension allows to investigate the high-spin band structures observed in odd-proton systems up to and including the second band crossing region, and as a first major application of this development, the high-spin properties are investigated for odd-mass $^{125-137}$Pr and $^{127-139}$Pm isotopes. It is shown that band crossings in the studied isotopes have mixed structures with first crossing dominated by one-proton coupled to two-neutron configuration for the lighter isotopes which then changes to three-proton configuration with increasing neutron number. Further, $γ$-bands based on quasiparticle states are also delineated in the present work, and it is predicted that these band structures built on three-quasiparticle configurations become favoured in energy for heavier systems in the high-spin region.

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arXiv2020

Triaxial projected shell model study of $γ$-bands in atomic nuclei

A systematic study of $γ$-bands observed in atomic nuclei is performed using the triaxial projected shell model (TPSM) approach. The staggering phase between the even and odd spin members of the $γ$-band for most the nuclei investigated in the present work is found to have even-I-below-odd-I, which in the framework of the collective model is considered as a signature of $γ$-softness. It is observed that out of twenty-three systems studied, only four nuclei, namely, $^{76}$Ge, $^{112}$Ru, $^{170}$Er and $^{232}$Th depict staggering phase with odd-I-below-even-I, which is regarded as an indication of the static $γ$-deformation in the collective model picture. The inclusion of the quasiparticle excitations in the framework of configuration mixing is shown to reverse the staggering phase from odd-I-down to the even-I-down for all the studied nuclei, except for the aforementioned four nuclei. Furthermore, by fitting a collective Bohr Hamiltonian to the TPSM energies, the differences between the two models are delineated through a comparison of the transition probabilities.

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